We also take advantage of a property of four-point tree-level amplitudes
noted in the original BCJ paper [1]}, which states that we can effectively set one of the three numerators to zero. In this way the duality relation
implies that the other two numerators
must be equal (up to a possible sign). In order to achieve that, we absorb the propagator of the diagram
whose numerator is set to zero into the numerators of the
other two diagrams. Specifically, consider the four-point all-gluon tree-level
amplitude,
\(\mathcal {A}_4^\text{tree} = g^2 \Bigl ( \frac{n_s c_s}{s} + \frac{n_t c_t}{t} + \frac{n_u c_u}{u} \Bigr ) \,.\) 
